Motivation

For severe storms, it is widely known that puncture damage is the primary cause of failure for most buildings and aircraft. Once a puncture has been created, the resultant pressure differential can cause fast inflow and damage to the interior. We seek to study this inflow, and stresses near the opening walls, which can cause structural issues leading to collapse of one or more walls.

Most relevant studies use incredibly large amounts of computational power, due to the large scale of the problem (Reynolds numbers for tornadoes and hurricanes can easily start in the millions). We seek to show the applicability of lower Reynolds simulations to higher Reynolds situations, since the general large-scale flow structure remains the same.

Mesh Assembly

We assemble a 2D mesh template as below, with the following parameters, all lengths nondimensionalized in terms of dimension \(L\):

mutable: wall thickness \(w\), window width \(a\),
immutable: window location \(b=0.5\), cavity height \(H=1\), cavity width \(L=1\), and free-stream width \(2e=0.1\).

Two sets of simulations are performed, one for the low Reynolds (\(Re\)) numbers of 10 and 200, which will be shown to be steady, and another for \(Re=1000, 10000\).

Each mesh also has a corresponding refinement, which is described by the \(meshFactor\) parameter, representing the refinement in each dimension.

Full lists are available below.

Literature Review

Wind speeds may be categorized as dangerous once reaching the threshold of 50mph. Winds of this caliber may occur during storms and tornados, and can be catastrophic to infrastructure.(2019; Hadhazy 2011; Tessner 2021)

Structurally, windows are weak in comparison to the surrounding structure and therefore are generally the first to break when confronted with strong winds. The missing window then creates a cavity with a pressure differential to the outside wind that may encourage further destruction. The fragility of windows is why many coastal buildings near hurricane hotspots have shutters, and in the event of a storm, those without shutters often cover their windows with materials such as plywood to protect against the oncoming winds.(2019; Hadhazy 2011; Tessner 2021)

The average home is designed to withstand winds of 90mph for around 3 seconds, which is far from sufficient to withstand even a moderate class of tornado. Especially when including forces working in tadem generating lift on top of normal stressors. As roof connections rely primarily on gravity to ensure stabiity, any opposing force to gravity need only overcome the weight force of the roof to remove it from the structure entirely.(2019; Hadhazy 2011; Tessner 2021)

Due to the propensity of air to create vortices when exposed to nonzero velocity and pressure differential, the way air may travel through the structure could pose an additional destructor on top of the exterior conditions. It has been proven advantageous for homes in storm-prone areas to install shutters, so prevention of inducing cavity-like flow on a structure is of import.(2019; Hadhazy 2011; Tessner 2021)

Low Reynolds Number

Note all values are nondimensionalized - all lengths are in terms of \(L\), the cavity length, all speeds in terms of \(U\), the initial flow speed, and all times in terms of \(\frac{L}{U}\).

The pressure is in terms of \(\frac{p}{\rho U^2}\).

High Reynolds Number Part 1

Note again all values are nondimensionalized - all lengths are in terms of \(L\), the cavity length, all speeds in terms of \(U\), the initial flow speed, and all times in terms of \(\frac{L}{U}\).

The pressure is in terms of \(\frac{p}{\rho U^2}\).

For spheres in uniform flow in the Reynolds number range of 8×10^2 < Re < 2×10^5 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake, is independent of the Reynolds number Re and is approximately equal to 0.2. The higher-frequency Strouhal number is caused by small-scale instabilities from the separation of the shear layer.[@vort1; @vort2]  

High Reynolds Number - Part 2